High-Performance Scientific Computing Applied Mathematics 483/583, - - PDF document

High-Performance Scientific Computing

Applied Mathematics 483/583, Spring 2013 University of Washington, Seattle Instructor: Randy LeVeque

http://faculty.washington.edu/rjl/classes/am583s2013/

https://canvas.uw.edu/courses/812916

More seats available today in room 206!

R.J. LeVeque, University of Washington AMath 483/583, Lecture 1

Notes:

R.J. LeVeque, University of Washington AMath 483/583, Lecture 1

Course logistics

Sections for UW students: in-class virtual

• nline Masters

AMath 483 A B AMath 583 A D B Also offered on Coursera this year, starting in May.

R.J. LeVeque, University of Washington AMath 483/583, Lecture 1

Notes:

R.J. LeVeque, University of Washington AMath 483/583, Lecture 1

Assignments and grading

See course webpage / class notes for schedule and assignments. 6 homework assignments, due Wednesday night. Final project, due Finals week. These will be turned in by pushing to a bitbucket repository. Short quiz associated with each lecture. Must be completed before the next lecture takes place! Will require seeing lecture and perhaps additional reading.

R.J. LeVeque, University of Washington AMath 483/583, Lecture 1

Notes:

R.J. LeVeque, University of Washington AMath 483/583, Lecture 1

Discussion board and other help

Please use the Piazza discussion board. Getting help from fellow students is a great way to learn. But... please don’t give detailed answers to assignments. You only should submit code that you have written and debugged yourself. Read and respect the honor code.

R.J. LeVeque, University of Washington AMath 483/583, Lecture 1

Notes:

R.J. LeVeque, University of Washington AMath 483/583, Lecture 1

TAs and office hours

Two TAs are available to all UW students: Scott Moe and Susie Sargsyan (AMath PhD students) Office hours: posted on Canvas course web page

https://canvas.uw.edu/courses/812916 Tentative: M 1:30-2:30 in Lewis 208, T 10:30-11:30 in Lewis 212 (*) W 1:30-2:30 in Lewis 208 (*) F 12:00-1:00 in Lewis 212 (*) GoToMeeting also available for 583B students My office hours: M & W in CSE Atrium, 9:30 – 10:45.

R.J. LeVeque, University of Washington AMath 483/583, Lecture 1

Notes:

R.J. LeVeque, University of Washington AMath 483/583, Lecture 1

Applied Math is now in Lewis Hall!

[map]

R.J. LeVeque, University of Washington AMath 483/583, Lecture 1

Notes:

R.J. LeVeque, University of Washington AMath 483/583, Lecture 1

Outline of this lecture

• Goals of this course, strategy for getting there
• Computer/software requirements
• Brief overview of material
• Demo and discussion on heat conduction problem

R.J. LeVeque, University of Washington AMath 483/583, Lecture 1

Notes:

R.J. LeVeque, University of Washington AMath 483/583, Lecture 1

Overview

High Performance Computing (HPC) often means heavy-duty computing on clusters or supercomputers with 100s of thousands of cores. “World’s fastest computer” #1. Titan (Oak Ridge National Lab): 560,640 cores, ≈ 20 Petaflops See http://top500.org for current list.

R.J. LeVeque, University of Washington AMath 483/583, Lecture 1

Notes:

R.J. LeVeque, University of Washington AMath 483/583, Lecture 1

Increasing speed

Moore’s Law: Processor speed doubles every 18 months. = ⇒ factor of 1024 in 15 years. Going forward: Number of cores doubles every 18 months. Top: Total computing power of top 500 com- puters Middle: #1 computer Bottom: #500 computer

http://www.top500.org

R.J. LeVeque, University of Washington AMath 483/583, Lecture 1

Notes:

R.J. LeVeque, University of Washington AMath 483/583, Lecture 1

Overview

Our focus is more modest, but we will cover material that is:

• Essential to know if you eventually want to work on

supercomputers,

• Extremely useful for any scientific computing project, even
• n a laptop.

Focus on scientific computing as opposed to other computationally demanding domains, for which somewhat different tools might be best.

R.J. LeVeque, University of Washington AMath 483/583, Lecture 1

Notes:

R.J. LeVeque, University of Washington AMath 483/583, Lecture 1

Focus and Topics

Efficiently using single processor and multi-core computers

• Basic computer architecture, e.g. floating point arithmetic,

cache hierarchies, pipelining

• Using Unix (or Linux, Mac OS X)
• Language issues, e.g. compiled vs. interpreted,
• bject oriented, etc.
• Specific languages: Python, Fortran 90/95
• Parallel computing with OpenMP

, MPI, IPython Efficient programming and good software practices

• Version control: Git, bitbucket
• Makefiles, Python scripting
• Debuggers, code development and testing
• Reproducibility

R.J. LeVeque, University of Washington AMath 483/583, Lecture 1

Notes:

R.J. LeVeque, University of Washington AMath 483/583, Lecture 1

Strategy

So much material, so little time....

• Concentrate on basics, simple motivating examples.
• Get enough hands-on experience to be comfortable

experimenting further and learning much more on your

• wn.
• Learn what’s out there to help select what’s best for your

needs.

• Teach many things “by example” as we go along.
• You’ll be expected to read notes and suggested readings.

Browse the bibliography in the notes.

R.J. LeVeque, University of Washington AMath 483/583, Lecture 1

Notes:

R.J. LeVeque, University of Washington AMath 483/583, Lecture 1

Strategy

So much material, so little time....

• Concentrate on basics, simple motivating examples.
• Get enough hands-on experience to be comfortable

experimenting further and learning much more on your

• wn.
• Learn what’s out there to help select what’s best for your

needs.

• Teach many things “by example” as we go along.
• You’ll be expected to read notes and suggested readings.

Browse the bibliography in the notes.

R.J. LeVeque, University of Washington AMath 483/583, Lecture 1

Notes:

R.J. LeVeque, University of Washington AMath 483/583, Lecture 1

Lecture notes

• html and pdf versions from class webpage

(green = link in pdf file)

• Written using Sphinx: Python-based system for writing

documentation.

• Learn by example!! Source for each file can be seen by

clicking on “Show Source” on right-hand menu.

• Source files are in class bitbucket repository. You can

clone the repository and run Sphinx yourself to make a local version.

$ git clone https://rjleveque@bitbucket.org/rjleveque/uwhpsc.git $ cd uwhpsc/notes $ make html $ firefox _build/html/index.html

R.J. LeVeque, University of Washington AMath 483/583, Lecture 1

Notes:

R.J. LeVeque, University of Washington AMath 483/583, Lecture 1

Lecture slides

Slides from lectures will be linked from the class webpage In single-slide form and 3-up form that has room for taking notes. Note: Slides will contain things not in the notes, lectures will also include hands-on demos not on the slides. Slides and notes are licensed using the CreativeCommons CC BY license: You can use them for any purpose as long as you include attribution.

R.J. LeVeque, University of Washington AMath 483/583, Lecture 1

Notes:

R.J. LeVeque, University of Washington AMath 483/583, Lecture 1

Prerequisites

Some programming experience in some language, e.g., Matlab, C, Java. You should be comfortable:

• editing a file containing a program and executing it,
• using basic structures like loops, if-then-else, input-output,
• writing subroutines or functions in some language

You are not expected to know Python or Fortran. Some basic knowledge of linear algebra, e.g.:

• what vectors and matrices are and how to multiply them
• How to go about solving a linear system of equations

Some comfort level for learning new sofware and willingness to dive in to lots of new things.

R.J. LeVeque, University of Washington AMath 483/583, Lecture 1

Notes:

R.J. LeVeque, University of Washington AMath 483/583, Lecture 1

Computer/Software requirements

You will need access to a computer with a number of things on it, see the section of the notes on Downloading and Installing Software. Note: Unix is often required for scientific computing. Windows: Many tools we’ll use can be used with Windows, but learning Unix is part of this class. Options:

• Install everything you’ll need on your own computer, or find

a computer with what you need.

• Install VirtualBox and use the Virtual Machine (VM)

created for this class.

• Use Amazon Web Services with the Amazon Machine

Image (AMI) created for this class.

R.J. LeVeque, University of Washington AMath 483/583, Lecture 1

Notes:

R.J. LeVeque, University of Washington AMath 483/583, Lecture 1

Demo...

$ git clone \ https://bitbucket.org/rjleveque/uwhpsc.git $ cd uwhpsc/lectures/lecture1 $ make plots $ firefox *.png

R.J. LeVeque, University of Washington AMath 483/583, Lecture 1

Notes:

R.J. LeVeque, University of Washington AMath 483/583, Lecture 1

Steady state heat conduction

Discretize on an N × N grid with N2 unknowns: Assume temperature is fixed (and known) at each point on boundary. At interior points, the steady state value is (approximately) the average of the 4 neighboring values.

R.J. LeVeque, University of Washington AMath 483/583, Lecture 1

Notes:

R.J. LeVeque, University of Washington AMath 483/583, Lecture 1

Steady state heat conduction

ui,j = 1 4(ui−1,j + ui+1,j + ui,j−1 + ui,j+1) Holds for i, j = 1, 2, . . . , N with u0,j known on boundary. Gives a linear system Au = b, with N2 equations N2 unknowns. Matrix A is N2 × N2, for N = 120, N2 = 14400. Very sparse: each row of matrix A has at most 5 nonzeros. Gaussian elimination is not the best approach. Jacobi iteration: (Also a poor method!) u[k+1]

i,j

= 1 4

• u[k]

i−1,j + u[k] i+1,j + u[k] i,j−1 + u[k] i,j+1

• R.J. LeVeque, University of Washington

AMath 483/583, Lecture 1

Notes:

R.J. LeVeque, University of Washington AMath 483/583, Lecture 1

Speedup for problems like steady state heat equation

Source: SIAM Review 43(2001), p. 168.

R.J. LeVeque, University of Washington AMath 483/583, Lecture 1

Notes:

R.J. LeVeque, University of Washington AMath 483/583, Lecture 1

Quiz on Lecture 1

Available later today on Canvas webpage:

https://canvas.uw.edu/courses/812916

R.J. LeVeque, University of Washington AMath 483/583, Lecture 1

Notes:

R.J. LeVeque, University of Washington AMath 483/583, Lecture 1

Class Virtual Machine

Available online from class webpage This file is large! About 765 MB compressed. After unzipping, about 2.2 GB. Also available from TAs on thumb drive during office hours, Or during class on Wednesday or Friday.

R.J. LeVeque, University of Washington AMath 483/583, Lecture 1

Notes:

R.J. LeVeque, University of Washington AMath 483/583, Lecture 1